Geodesic
Adapted downhill simplex method for pricing convertible bonds
Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 130-147.

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The paper is devoted to modeling optimal exercise strategies of the behavior of investors and issuers working with convertible bonds. This implies solution of the problems of stock price modeling, payoff computation and minimax optimization. Stock prices (underlying asset) were modeled under the assumption of the geometric Brownian motion of their values. The Monte Carlo method was used for calculating the real payoff which is the objective function. The minimax optimization problem was solved using the derivative-free Downhill Simplex method. The performed numerical experiments allowed to formulate recommendations for the choice of appropriate size of the initial simplex in the Downhill Simplex Method, the number of generated trajectories of underlying asset, the size of the problem and initial trajectories of the behavior of investors and issuers.
Keywords: Convertible bonds, optimal strategies, Downhill Simplex method, minimax optimization problem.
Mots-clés : Monte Carlo simulation 
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Kateryna Mishchenko; Volodymyr Mishchenko; Anatoliy Malyarenko. Adapted downhill simplex method for pricing convertible bonds. Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 130-147. http://geodesic.mathdoc.fr/item/THSP_2007_13_4_a7/

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